Australia Telescope National Facility

Cosmological Parameter Survey Using the Gravitational Lensing Method
Premana W Premadi , Hugo Martel , Richard Matzner , Toshifumi Futamase, PASA, 18 (2), in press.

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The Ray-Tracing Experiments

To simulate light propagation in inhomogeneous universes, we use a newly developed version of the Multiple Lens-Plane Algorithm (Schneider, Ehlers, and Falco (1992), Jaroszynsky 1992, Martel, Premadi, and Matzner (1998), Premadi, Martel, and Matzner (1998)). Our algorithm uses a $\rm P^3M$ code with 64³ particles to simulate the formation and evolution of large-scale structure in the universe inside a computational volume of comoving size

$L_{\rm box}=128\,\rm Mpc$ . The result is then used as the underlying distribution of dark matter in locating galaxies inside the computational volume by using an empirical Monte Carlo method. Each galaxy is modeled by a truncated, non-singular isothermal sphere. By combining the distribution of background matter simulated by the P³M algorithm with the distribution and surface densities of galaxies, we effectively describe the surface density of the lens planes over 8 orders of magnitude in length, from the size of the largest superclusters and voids,

$\sim100\,\rm Mpc$ , down to the core radii of the smallest galaxies, $\sim1\,\rm pc$ .

We consider Tilted Cold Dark Matter models (TCDM), normalized to COBE. The power spectrum for this model is characterized by 6 independent parameters: $\Omega _0$ ,

$\Omega_{\rm B0}$ (the density parameter of the baryonic matter), $\lambda _0$ , H₀, $T_{\rm CMB}$ (the temperature of the cosmic microwave background), and n. The normalization of the power spectrum is often described in terms of the rms density fluctuation $\sigma _8$ at a scale of

$8h^{-1}\rm Mpc$ . The value of $\sigma _8$ is a function of the 6 aforementioned parameters. We invert this relation, treating $\sigma _8$ as an independent parameter, and the tilt n as a dependent one. We also set

$T_{\rm CMB}=2.7\,\rm K$ and

$\Omega_{\rm B0}=0.015h^{-2}$ . The independent parameters in this parameter space are therefore $\Omega _0$ , $\lambda _0$ , H₀, and $\sigma _8$ . We survey this parameter space by considering 43 different cosmological models. The values of the parameters are listed in Table 1. For each model, we performed from 50 to 200 ray-tracing experiments (depending on the statistical significance of the results) for a total of 3798 experiments. In each experiment, we compute the propagation of a beam consisting of 341²=116,281 light rays forming a square lattice on the image plane. The size of the beam is

$21.9''\times21.9''$ , and the separation between rays is

21.9''/341=0.064''. The beams are propagated from redshift z=0 to $z\sim3$ (sources at redshifts z>3 would produce qualitatively similar results).

Next Section: The Elements of Gravitational
Title/Abstract Page: Cosmological Parameter Survey Using
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Contents Page: Volume 18, Number 2

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